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Let's solve the multiplication and simplify the given expression step by step.

We are given:

\[
2w^6 \cdot 3u^2 \cdot w^8 \cdot 8u
\]

### Step 1: Multiply the coefficients
We multiply the numerical coefficients first: \(2 \cdot 3 \cdot 8\).

\[
2 \times 3 \times 8 = 48
\]

### Step 2: Combine the variables with the same base
- For \(w\), we have \(w^6\) and \(w^8\). We apply the law of exponents \((a^m \cdot a^n = a^{m+n})\):

\[
w^6 \cdot w^8 = w^{6+8} = w^{14}
\]

- For \(u\), we have \(u^2\) and \(u\). Remember that \(u\) is the same as \(u^1\), so:

\[
u^2 \cdot u^1 = u^{2+1} = u^3
\]

### Step 3: Write the simplified expression
Now that we have simplified both the coefficients and the variables, the expression becomes:

\[
48w^{14}u^3
\]

This is the fully simplified answer.

Would you like more details on any step, or do you have any questions?

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Here are 5 related questions to expand on this concept:
1. What is the general rule for multiplying powers with the same base?
2. How would the solution change if the powers had negative exponents?
3. Can you demonstrate how to multiply expressions with different variables, like \(x^3 \cdot y^2\)?
4. What would happen if one of the coefficients was negative?
5. How would you simplify a division involving exponents, such as \(\frac{w^6}{w^2}\)?

**Tip:** When multiplying variables with exponents, always remember to add the exponents, not multiply them!

Multiply and simplify the expression 2w^6 · 3u^2 · w^8 · 8u.

Learn how to multiply and simplify expressions with exponents and coefficients, such as 2w^6 · 3u^2 · w^8 · 8u. This step-by-step solution demonstrates how to use exponent rules and multiply constants, suitable for students in Grades 8-10.

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